基于灰色关联与自适应参考向量的高维多目标进化算法
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TP273

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国家自然科学基金青年基金项目(62106088).


Grey relation-based evolutionary algorithm with self-adaptive reference vectors for many-objective optimization
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    摘要:

    针对高维多目标优化问题中普遍存在的解集多样性维持困难、收敛性不足及复杂帕累托前沿适应性差等挑战, 提出一种基于灰色关联与自适应参考向量的高维多目标进化算法. 首先, 针对多样性和收敛性平衡问题, 提出一种基于灰色关联度的环境选择策略, 该策略通过灰色相似关联度衡量种群在目标空间的分布差异, 同时采用灰色接近关联度量化解与理想点的空间距离. 前者用于维持多样性, 后者能够保证收敛性. 在此基础上, 设计一种参考向量自适应更新策略, 通过动态生成新向量与周期性删减冗余向量, 追踪复杂帕累托前沿的拓扑演化. 实验结果表明, 在9个DTLZ系列基准问题和2个实际工程问题中, 所提算法在收敛性和多样性方面均显著优于其他4个代表性对比算法.

    Abstract:

    To address the challenges of maintaining solution diversity, insufficient convergence, and inadequate adaptability to complex Pareto fronts in many-objective optimization problems, this paper proposes a grey relation-based evolutionary algorithm with self-adaptive reference vectors. First, to balance the diversity and convergence, a novel environmental selection strategy based on grey relational degree is proposed. This strategy employs grey similitude relational degree to measure distribution differences of solutions in the objective space, and adopts grey closeness relational degree to quantify the spatial distance between solutions and the ideal point. The former maintains diversity, whereas the latter ensures convergence. Then, a reference vector adaptation strategy is developed to track the topological evolution of complex Pareto fronts through dynamic insertion of new vectors and periodic deletion of redundant vectors. Experimental results on 9 DTLZ benchmark problems and two real-world cases demonstrate that the proposed algorithm significantly outperforms four other state-of-the-art algorithms in both convergence and diversity metrics.

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曾骏驰,张欣,钱鹏江,等.基于灰色关联与自适应参考向量的高维多目标进化算法[J].控制与决策,2026,41(1):153-164

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  • 收稿日期:2025-05-24
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  • 在线发布日期: 2025-12-30
  • 出版日期: 2026-01-10
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